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mr_godi [17]
3 years ago
12

Sara plotted the locations of the trees in a park on a coordinate grid. She plotted an oak tree which was in the middle of the p

ark at the origin.
Mathematics
1 answer:
padilas [110]3 years ago
8 0

Answer: 10.2\ yards

Step-by-step explanation:

<h3> "Sara plotted the locations of the trees in a park on a coordinate grid. She plotted an oak tree, which was in the middle of the park, at the origin. She plotted a maple tree, which was 10 yards away from the oak tree, at the point (10,0) . Then she plotted a pine tree at the point (-2.4, 5) and an apple tree at the point (7.8, 5) What is the distance, in yards, between the pine tree and the apple tree in the</h3><h3>park?"</h3>

For this exercise you need to use the following formula, which can be used for calculate the distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

In this case, you need to find distance, in yards, between the pine tree and the apple tree in the park.

You know that pine tree is located at the point (-2.4, 5) and the apple tree is located at the point (7.8, 5).

So, you can say that:

x_2=-2.4\\x_1=7.8\\\\y_2=5\\y_1=5

Knowing these values, you can substitute them into the formula and then evaluate, in order to find the distance, in yards, between the pine tree and the apple tree in the park.

This is:

d=\sqrt{(-2.4-7.8)^2+(5-5)^2}=10.2\ yards

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<em><u>The inequality can be used to find the interval of time taken by the object to reach the height  greater than 300 feet above the ground is:</u></em>

d = -16t^2 + 1000

<em><u>Solution:</u></em>

<em><u>The object falls, its distance, d, above the ground after t seconds, is given by the  formula:</u></em>

d = -16t^2 + 1000

To find the time interval in which the object is at a height greater than 300 ft

Frame a inequality,

-16t^2 + 1000 > 300

Solve the inequality

Subtract 1000 from both sides

-16t^2 + 1000 - 1000 > 300 - 1000\\\\-16t^2 > -700

16t^2 < 700\\\\Divide\ both\ sides\ by\ 16\\\\t^2 < \frac{700}{16}\\\\Take\ square\ root\ on\ both\ sides\\\\t < \sqrt{\frac{700}{16}}\\\\t < \pm 6.61

Time cannot be negative

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t < 6.61

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6 0
3 years ago
In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 r
iren2701 [21]

Answer:

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Step-by-step explanation:

Given

In 1990; Income= $39000

In 2010; Income= $70768

Solving (a): An equation in form of f(x) = ax + b

First, we need to determine the slope, a

a = \frac{y_2 - y_1}{x_2 - x_1}

Taking y as income and x as year index.

When x = 0; y = 39000

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Substitute these values in the above formula

a = \frac{70768 - 39000}{20 - 0}

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Next, is to determine the formula using:

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<em>Considering :When x = 0; y = 39000, we have</em>

<em />y - 39000 = 1588.4(x - 0)<em />

<em />y - 39000 = 1588.4x<em />

<em>Make y the subject of formula</em>

<em />y = 1588.4x + 39000<em />

<em />

<em>Express y as a function of x</em>

<em />f(x) = 1588.4x + 39000<em />

Solving (b): Income in 2005

<em>In 2005, x = 15</em>

So:

f(x) = 1588.4x + 39000 becomes

f(15) = 1588.4 * 15 + 39000

f(15) = 62826

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3 years ago
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